Dynamics Reported: Expositions in Dynamical Systems: Dynamics Reported. New Series, cartea 5
Contribuţii de N. Fenichel, P. Koch Medina, D.W. McLaughlin, X. Lin, E.A.II Overman, S. Wiggins, C. Xiongen Limba Engleză Paperback – 14 dec 2011
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Specificații
ISBN-13: 9783642799334
ISBN-10: 3642799337
Pagini: 304
Ilustrații: IX, 287 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.43 kg
Ediția:Softcover reprint of the original 1st ed. 1996
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Dynamics Reported. New Series
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3642799337
Pagini: 304
Ilustrații: IX, 287 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.43 kg
Ediția:Softcover reprint of the original 1st ed. 1996
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Dynamics Reported. New Series
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
ResearchCuprins
Hyperbolicity and Exponential Dichotomy for Dynamical Systems.- 1. Introduction.- 2. The Main Lemma.- 3. The Linearization Theorem of Hartman and Grobman.- 4. Hyperbolic Invariant Sets: e-orbits and Stable Manifolds.- 5. Structural Stability of Anosov Diffeomorphisms.- 6. Periodic Points of Anosov Diffeomorphisms.- 7. Axiom A Diffeomorphisms: Spectral Decomposition.- 8. The In-Phase Theorem.- 9. Flows.- 10. Proof of Lemma 1.- References.- Feedback Stabilizability of Time-Periodic ParabolicEquations.- 0. Introduction.- I. Linear Periodic Evolution Equations.- II. Controllability, Observability and Feedback Stabilizability.- III. Applications to Second Order Time-Periodic Parabolic Initial-Boundary Value Problems.- References.- Homoclinic Bifurcations with Weakly Expanding Center.- 1. Introduction.- 2. Hypotheses, a Reduction Principle and Basic Existence Theorems.- 3. Preliminaries.- 4. Proof of the Main Results in 2.- 5. Simple Periodic Solutions.- 6. Bifurcations of Homoclinic Solutions with One-Dimensional Local Center Manifolds.- 7. Estimates Related to a Nondegenerate Hopf Bifurcation.- 8. Interaction of Homoclinic Bifurcation and Hopf Bifurcation.- 9. The Disappearance of Periodic and Aperiodic Solutions when ?2 Passes Through Turning Points.- References.- Homoclinic Orbits in a Four Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study.- 1. Introduction.- 2. Geometric Structure and Dynamics of the Unperturbed System.- 3. Geometric Structure and Dynamics of the Perturbed System.- 4. Fiber Representations of Stable and Unstable Manifolds.- 5. Orbits Homoclinic to q€.- 6. Numerical Study of Orbits Homoclinic to q€.- 7. The Dynamical Consequences of Orbits Homoclinic to q€: The Existence and Nature of Chaos.- 8. Conclusion.-References.
Textul de pe ultima copertă
This book contains four excellent contributions on topics in dynamical systems by authors with an international reputation: "Hyperbolic and Exponential Dichotomy for Dynamical Systems", "Feedback Stabilizability of Time-periodic Parabolic Equations", "Homoclinic Bifurcations with Weakly Expanding Center Manifolds" and "Homoclinic Orbits in a Four-Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study". All the authors give a careful and readable presentation of recent research results, addressed not only to specialists but also to a broader range of readers including graduate students.